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A322858 List of e-perfect numbers that are not e-unitary perfect. 2
17424, 87120, 121968, 226512, 296208, 331056, 400752, 505296, 540144, 609840, 644688, 714384, 749232, 818928, 923472, 1028016, 1062864, 1132560, 1167408, 1237104, 1271952, 1306800, 1376496, 1446192, 1481040, 1550736, 1585584, 1655280, 1690128, 1759824 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The e-unitary perfect numbers are numbers k such that the sum of their exponential unitary divisors (A322857) equals 2k. Apparently most of the e-perfect numbers (A054979) are also e-unitary perfect numbers: the first 150 e-perfect numbers are also the first 150 e-unitary perfect numbers. But A054979(151) = 17424 is not e-unitary perfect.

Minculete and Tóth ask if there is any e-unitary perfect number which is not e-perfect.

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

Nicusor Minculete and László Tóth, Exponential unitary divisors, Annales Univ. Sci. Budapest., Sect. Comp., Vol. 35 (2011), pp. 205-216.

MATHEMATICA

f[p_, e_] := DivisorSum[e, p^# &]; esigma[n_] := Times @@ f @@@ FactorInteger[n]; ePerfectQ[n_] := esigma[n] == 2n; fu[p_, e_] := DivisorSum[e, p^# &, GCD[#, e/#]==1 &]; eusigma[n_] := Times @@ fu @@@ FactorInteger[n]; euPerfectQ[n_] := eusigma[n] == 2n; aQ[n_] := ePerfectQ[n] && !euPerfectQ[n]; Select[Range[125000], aQ]

CROSSREFS

Cf. A051377, A054979, A322857.

Sequence in context: A219325 A255780 A023942 * A251465 A278004 A031640

Adjacent sequences:  A322855 A322856 A322857 * A322859 A322860 A322861

KEYWORD

nonn

AUTHOR

Amiram Eldar, Dec 29 2018

STATUS

approved

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Last modified September 19 16:24 EDT 2021. Contains 347564 sequences. (Running on oeis4.)